Atkin-Lehner |
2+ 3- 13+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
33072f |
Isogeny class |
Conductor |
33072 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
5376 |
Modular degree for the optimal curve |
Δ |
-6878976 = -1 · 28 · 3 · 132 · 53 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 -2 13+ -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,36,-84] |
[a1,a2,a3,a4,a6] |
Generators |
[11:42:1] [38:240:1] |
Generators of the group modulo torsion |
j |
19600688/26871 |
j-invariant |
L |
8.9793570108811 |
L(r)(E,1)/r! |
Ω |
1.2584854888669 |
Real period |
R |
7.1350500981675 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
16536a1 99216h1 |
Quadratic twists by: -4 -3 |